Henrik Madsen - Academia.edu (original) (raw)
Papers by Henrik Madsen
IEEE PES ISGT Europe 2013, 2013
ABSTRACT This paper presents a study of models for forecasting the load for supermarket refrigera... more ABSTRACT This paper presents a study of models for forecasting the load for supermarket refrigeration. The data used for building the forecasting models consists of load measurements, local climate measurements and weather forecasts. The load measurements are from a supermarket located in a village in Denmark. Every hour the hourly load for refrigeration for the following 42 hours is forecasted. The forecast models are time adaptive linear time-series models. The dynamic relations between the inputs and the load is modeled by simple transfer functions. The system operates in two regimes: one in the closing hours during night and one in the opening hours during the day. This is modeled by a regime switching model in which some of the coefficients in the model depends on the regime. The results show that the one-step ahead residuals are close to white noise, however it is found that some non-linear dependence on the ambient temperature should be included in the model in further work.
Water Research, 2002
A model of the concentrations of suspended solids (SS) in the aeration tanks and in the effluent ... more A model of the concentrations of suspended solids (SS) in the aeration tanks and in the effluent from these during Aeration tank settling (ATS) operation is established. The model is based on simple SS mass balances, a model of the sludge settling and a simple model of how the SS concentration in the effluent from the aeration tanks depends on the actual concentrations in the tanks and the sludge blanket depth. The model is formulated in continuous time by means of stochastic differential equations with discrete-time observations. The parameters of the model are estimated using a maximum likelihood method from data from an alternating BioDenipho waste water treatment plant (WWTP). The model is an important tool for analyzing ATS operation and for selecting the appropriate control actions during ATS, as the model can be used to predict the SS amounts in the aeration tanks as well as in the effluent from the aeration tanks.
2013 European Control Conference (ECC)
The method described in this paper balances power production and consumption with a large number ... more The method described in this paper balances power production and consumption with a large number of thermal loads. Linear controllers are used for the loads to track a temperature set point, while Model Predictive Control (MPC) and model estimation of the load behavior are used for coordination. The total power consumption of all loads is controlled indirectly through a real-time price. The MPC incorporates forecasts of the power production and disturbances that influence the loads, e.g. time-varying weather forecasts, in order to react ahead of time. A simulation scenario demonstrates that the method allows for the integration of flexible thermal loads in a smart energy system in which consumption follows the changing production.
Journal of Hydrology, 2014
We investigate the application of rainfall observations and forecasts from rain gauges and weathe... more We investigate the application of rainfall observations and forecasts from rain gauges and weather radar as input to operational urban runoff forecasting models. We apply lumped rainfall runoff models implemented in a stochastic grey-box modelling framework. Different model structures are considered that account for the spatial distribution of rainfall in different degrees of detail. Considering two urban example catchments, we show that statically adjusted radar rainfall input improves the quality of probabilistic runoff forecasts as compared to
Applied Energy, 2016
This paper presents a study of models for forecasting the electrical load for supermarket refrige... more This paper presents a study of models for forecasting the electrical load for supermarket refrigeration. The data used for building the models consists of load measurements, local climate measurements and weather forecasts. The load measurements are from a supermarket located in a village in Denmark. Every hour the hourly electrical load for refrigeration is forecasted for the following 42 hours. The forecast models are adaptive linear time series models. The model has two regimes; one for opening hours and one for closing hours, this is modelled by a regime switching model and two different methods for predicting the regimes are tested. The dynamic relation between the weather and the load is modelled by simple transfer functions and the non-linearities are described using spline functions. The results are thoroughly evaluated and it is shown that the spline functions are suitable for handling the nonlinear relations and that after applying an auto-regressive noise model the one-step ahead residuals do not contain further significant information.
IEEE Transactions on Smart Grid, 2016
Integration of a large number of flexible consumers in a smart grid requires a scalable power bal... more Integration of a large number of flexible consumers in a smart grid requires a scalable power balancing strategy. We formulate the control problem as an optimization problem to be solved repeatedly by the aggregator in a model predictive control framework. To solve the large-scale control problem in real-time requires decomposition methods. We propose a decomposition method based on Douglas-Rachford splitting to solve this largescale control problem. The method decomposes the problem into smaller subproblems that can be solved in parallel, e.g., locally by each unit connected to an aggregator. The total power consumption is controlled through a negotiation procedure between all cooperating units and an aggregator that coordinates the overall objective. For large-scale systems, this method is faster than solving the original problem and can be distributed to include an arbitrary number of units. We show how different aggregator objectives are implemented and provide simulations of the controller including the computational performance.
European Journal of Operational Research, 2009
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
IEEE PES ISGT Europe 2013, 2013
A power balancing strategy based on Douglas-Rachford splitting is proposed as a control method fo... more A power balancing strategy based on Douglas-Rachford splitting is proposed as a control method for large-scale integration of flexible consumers in a Smart Grid. The total power consumption is controlled through a negotiation procedure between all units and a coordinating system level. The balancing problem is formulated as a centralized large-scale optimization problem but is then decomposed into smaller subproblems that are solved locally by each unit connected to an aggregator. For large-scale systems the method is faster than solving the full problem and can be distributed to include an arbitrary number of units.
2012 IEEE International Electric Vehicle Conference, 2012
When containers are transported on a-modal bookings, the transport supplier can decide which comb... more When containers are transported on a-modal bookings, the transport supplier can decide which combination of trucks, trains, ships, etc. to use. This gives the flexibility to transport suppliers to route the containers in accordance with the current state of the synchromodal transport network. At the same time, it enables the transport providers to route their vehicles in real time based on the current need for transportation. The interdependency of the routes of containers and of vehicles has not yet been discussed explicitly in the synchromodal literature. The aim of this paper is thus to illustrate the effect of planning the routes of containers and trucks as one integrated problem. This is addressed with a model predictive control planning method. Simulation experiments of a synchromodal hinterland network are used to illustrate the method's potential.
IFAC Proceedings Volumes, 1996
This paper describes a new method for improving the control of air temperature in greenhouses. Th... more This paper describes a new method for improving the control of air temperature in greenhouses. The proposed controller is an extended version of the generalized predictive controller (GPC). The prediction of air temperature is facilitated by • continuous time stochastic state space model identified for the heat dynamics of the greenhouse. A simulation study illustrates that the proposed GPC gives a more active controller with less control error than the implemented PID controller.
Merging of radar rainfall data with rain gauge measurements is a common approach to overcome prob... more Merging of radar rainfall data with rain gauge measurements is a common approach to overcome problems in deriving rain intensities from radar measurements. We extend an existing approach for adjustment of C-band radar data using state-space models and use the resulting rainfall intensities as input for forecasting outflow from two catchments in the Copenhagen area. Stochastic greybox models are applied to create the runoff forecasts, providing us with not only a point forecast but also a quantification of the forecast uncertainty. Evaluating the results, we can show that using the adjusted radar data improves runoff forecasts compared to using the original radar data and that rain gauge measurements as forecast input are also outperformed. Combining the data merging approach with short term rainfall forecasting algorithms may result in further improved runoff forecasts that can be used in real time control.
Journal of Wind Engineering and Industrial Aerodynamics, 2008
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
Journal of Theoretical Biology, 2005
The present work introduces an extension of the original minimal model of second phase insulin se... more The present work introduces an extension of the original minimal model of second phase insulin secretion during the intravenous glucose tolerance test (IVGTT), which can provide both physiological and mathematical insights to the minimal model. The extension is named the mean-field beta cell model since it returns the average response of a large number of nonlinear secretory entities. Several secretion models have been proposed for the IVGTT, and we shall identify two fundamentally different theoretical features of these models. Both features can play a central role during the IVGTT, including the one presented in the mean-field beta cell model.
Journal of Microbiological Methods, 2008
The specific growth rate for P. aeruginosa and four mutator strains mutT, mutY, mutM and mutY-mut... more The specific growth rate for P. aeruginosa and four mutator strains mutT, mutY, mutM and mutY-mutM is estimated by a suggested Maximum Likelihood, ML, method which takes the autocorrelation of the observation into account. For each bacteria strain, six wells of optical density, OD, measurements are used for parameter estimation. The data is log-transformed such that a linear model can be applied. The transformation changes the variance structure, and hence an OD-dependent variance is implemented in the model. The autocorrelation in the data is demonstrated, and a correlation model with an exponentially decaying function of the time between observations is suggested. A model with a full covariance structure containing OD-dependent variance and an autocorrelation structure is compared to a model with variance only and with no variance or correlation implemented. It is shown that the model that best describes data is a model taking into account the full covariance structure. An inference study is made in order to determine whether the growth rate of the five bacteria strains is the same. After applying a likelihood-ratio test to models with a full covariance structure, it is concluded that the specific growth rate is the same for all bacteria strains. This study highlights the importance of carrying out an explorative examination of residuals in order to make a correct parametrization of a model including the covariance structure. The ML method is shown to be a strong tool as it enables estimation of covariance parameters along with the other model parameters and it makes way for strong statistical tools for inference studies.
IEEE Transactions on Power Systems, 2013
In a real-time electricity pricing context where consumers are sensitive to varying prices, havin... more In a real-time electricity pricing context where consumers are sensitive to varying prices, having the ability to anticipate their response to a price change is valuable. This paper proposes models for the dynamics of such price-response, and shows how these dynamics can be used to control electricity consumption using a one-way price signal. Estimation of the price-response is based on data measurable at grid level, removing the need to install sensors and communication devices between each individual consumer and the price-generating entity. An application for price-responsive heating systems is studied based on real data, before conducting a control by price experiment using a mixture of real and synthetic data. With the control objective of following a constant consumption reference, peak heating consumption is reduced by nearly 5%, and 11% of the mean daily heating consumption is shifted.
Environmetrics, 1996
Data from a stream is used to identify a dynamic model of the oxygen level as a function of solar... more Data from a stream is used to identify a dynamic model of the oxygen level as a function of solar radiation and precipitation. The time series of the oxygen level is occasionally corrupted by pumping of external water into the stream, which is of no interest to the biological processes in the stream. In this paper a grey box modelling approach, which is a statistical method taking the known physical relations into account, is used. Using this approach, an identification of a stochastic continuous time model for the oxygen level based on the discrete time data, where the corrupted data are considered as missing values, is outlined. KEY WORDS oxygen dynamics; time series analysis; missing data; continuous time modelling; grey box models
IEEE PES ISGT Europe 2013, 2013
ABSTRACT This paper presents a study of models for forecasting the load for supermarket refrigera... more ABSTRACT This paper presents a study of models for forecasting the load for supermarket refrigeration. The data used for building the forecasting models consists of load measurements, local climate measurements and weather forecasts. The load measurements are from a supermarket located in a village in Denmark. Every hour the hourly load for refrigeration for the following 42 hours is forecasted. The forecast models are time adaptive linear time-series models. The dynamic relations between the inputs and the load is modeled by simple transfer functions. The system operates in two regimes: one in the closing hours during night and one in the opening hours during the day. This is modeled by a regime switching model in which some of the coefficients in the model depends on the regime. The results show that the one-step ahead residuals are close to white noise, however it is found that some non-linear dependence on the ambient temperature should be included in the model in further work.
Water Research, 2002
A model of the concentrations of suspended solids (SS) in the aeration tanks and in the effluent ... more A model of the concentrations of suspended solids (SS) in the aeration tanks and in the effluent from these during Aeration tank settling (ATS) operation is established. The model is based on simple SS mass balances, a model of the sludge settling and a simple model of how the SS concentration in the effluent from the aeration tanks depends on the actual concentrations in the tanks and the sludge blanket depth. The model is formulated in continuous time by means of stochastic differential equations with discrete-time observations. The parameters of the model are estimated using a maximum likelihood method from data from an alternating BioDenipho waste water treatment plant (WWTP). The model is an important tool for analyzing ATS operation and for selecting the appropriate control actions during ATS, as the model can be used to predict the SS amounts in the aeration tanks as well as in the effluent from the aeration tanks.
2013 European Control Conference (ECC)
The method described in this paper balances power production and consumption with a large number ... more The method described in this paper balances power production and consumption with a large number of thermal loads. Linear controllers are used for the loads to track a temperature set point, while Model Predictive Control (MPC) and model estimation of the load behavior are used for coordination. The total power consumption of all loads is controlled indirectly through a real-time price. The MPC incorporates forecasts of the power production and disturbances that influence the loads, e.g. time-varying weather forecasts, in order to react ahead of time. A simulation scenario demonstrates that the method allows for the integration of flexible thermal loads in a smart energy system in which consumption follows the changing production.
Journal of Hydrology, 2014
We investigate the application of rainfall observations and forecasts from rain gauges and weathe... more We investigate the application of rainfall observations and forecasts from rain gauges and weather radar as input to operational urban runoff forecasting models. We apply lumped rainfall runoff models implemented in a stochastic grey-box modelling framework. Different model structures are considered that account for the spatial distribution of rainfall in different degrees of detail. Considering two urban example catchments, we show that statically adjusted radar rainfall input improves the quality of probabilistic runoff forecasts as compared to
Applied Energy, 2016
This paper presents a study of models for forecasting the electrical load for supermarket refrige... more This paper presents a study of models for forecasting the electrical load for supermarket refrigeration. The data used for building the models consists of load measurements, local climate measurements and weather forecasts. The load measurements are from a supermarket located in a village in Denmark. Every hour the hourly electrical load for refrigeration is forecasted for the following 42 hours. The forecast models are adaptive linear time series models. The model has two regimes; one for opening hours and one for closing hours, this is modelled by a regime switching model and two different methods for predicting the regimes are tested. The dynamic relation between the weather and the load is modelled by simple transfer functions and the non-linearities are described using spline functions. The results are thoroughly evaluated and it is shown that the spline functions are suitable for handling the nonlinear relations and that after applying an auto-regressive noise model the one-step ahead residuals do not contain further significant information.
IEEE Transactions on Smart Grid, 2016
Integration of a large number of flexible consumers in a smart grid requires a scalable power bal... more Integration of a large number of flexible consumers in a smart grid requires a scalable power balancing strategy. We formulate the control problem as an optimization problem to be solved repeatedly by the aggregator in a model predictive control framework. To solve the large-scale control problem in real-time requires decomposition methods. We propose a decomposition method based on Douglas-Rachford splitting to solve this largescale control problem. The method decomposes the problem into smaller subproblems that can be solved in parallel, e.g., locally by each unit connected to an aggregator. The total power consumption is controlled through a negotiation procedure between all cooperating units and an aggregator that coordinates the overall objective. For large-scale systems, this method is faster than solving the original problem and can be distributed to include an arbitrary number of units. We show how different aggregator objectives are implemented and provide simulations of the controller including the computational performance.
European Journal of Operational Research, 2009
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
IEEE PES ISGT Europe 2013, 2013
A power balancing strategy based on Douglas-Rachford splitting is proposed as a control method fo... more A power balancing strategy based on Douglas-Rachford splitting is proposed as a control method for large-scale integration of flexible consumers in a Smart Grid. The total power consumption is controlled through a negotiation procedure between all units and a coordinating system level. The balancing problem is formulated as a centralized large-scale optimization problem but is then decomposed into smaller subproblems that are solved locally by each unit connected to an aggregator. For large-scale systems the method is faster than solving the full problem and can be distributed to include an arbitrary number of units.
2012 IEEE International Electric Vehicle Conference, 2012
When containers are transported on a-modal bookings, the transport supplier can decide which comb... more When containers are transported on a-modal bookings, the transport supplier can decide which combination of trucks, trains, ships, etc. to use. This gives the flexibility to transport suppliers to route the containers in accordance with the current state of the synchromodal transport network. At the same time, it enables the transport providers to route their vehicles in real time based on the current need for transportation. The interdependency of the routes of containers and of vehicles has not yet been discussed explicitly in the synchromodal literature. The aim of this paper is thus to illustrate the effect of planning the routes of containers and trucks as one integrated problem. This is addressed with a model predictive control planning method. Simulation experiments of a synchromodal hinterland network are used to illustrate the method's potential.
IFAC Proceedings Volumes, 1996
This paper describes a new method for improving the control of air temperature in greenhouses. Th... more This paper describes a new method for improving the control of air temperature in greenhouses. The proposed controller is an extended version of the generalized predictive controller (GPC). The prediction of air temperature is facilitated by • continuous time stochastic state space model identified for the heat dynamics of the greenhouse. A simulation study illustrates that the proposed GPC gives a more active controller with less control error than the implemented PID controller.
Merging of radar rainfall data with rain gauge measurements is a common approach to overcome prob... more Merging of radar rainfall data with rain gauge measurements is a common approach to overcome problems in deriving rain intensities from radar measurements. We extend an existing approach for adjustment of C-band radar data using state-space models and use the resulting rainfall intensities as input for forecasting outflow from two catchments in the Copenhagen area. Stochastic greybox models are applied to create the runoff forecasts, providing us with not only a point forecast but also a quantification of the forecast uncertainty. Evaluating the results, we can show that using the adjusted radar data improves runoff forecasts compared to using the original radar data and that rain gauge measurements as forecast input are also outperformed. Combining the data merging approach with short term rainfall forecasting algorithms may result in further improved runoff forecasts that can be used in real time control.
Journal of Wind Engineering and Industrial Aerodynamics, 2008
Users may download and print one copy of any publication from the public portal for the purpose... more Users may download and print one copy of any publication from the public portal for the purpose of private study or research. You may not further distribute the material or use it for any profit-making activity or commercial gain You may freely distribute the URL identifying the publication in the public portal If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim.
Journal of Theoretical Biology, 2005
The present work introduces an extension of the original minimal model of second phase insulin se... more The present work introduces an extension of the original minimal model of second phase insulin secretion during the intravenous glucose tolerance test (IVGTT), which can provide both physiological and mathematical insights to the minimal model. The extension is named the mean-field beta cell model since it returns the average response of a large number of nonlinear secretory entities. Several secretion models have been proposed for the IVGTT, and we shall identify two fundamentally different theoretical features of these models. Both features can play a central role during the IVGTT, including the one presented in the mean-field beta cell model.
Journal of Microbiological Methods, 2008
The specific growth rate for P. aeruginosa and four mutator strains mutT, mutY, mutM and mutY-mut... more The specific growth rate for P. aeruginosa and four mutator strains mutT, mutY, mutM and mutY-mutM is estimated by a suggested Maximum Likelihood, ML, method which takes the autocorrelation of the observation into account. For each bacteria strain, six wells of optical density, OD, measurements are used for parameter estimation. The data is log-transformed such that a linear model can be applied. The transformation changes the variance structure, and hence an OD-dependent variance is implemented in the model. The autocorrelation in the data is demonstrated, and a correlation model with an exponentially decaying function of the time between observations is suggested. A model with a full covariance structure containing OD-dependent variance and an autocorrelation structure is compared to a model with variance only and with no variance or correlation implemented. It is shown that the model that best describes data is a model taking into account the full covariance structure. An inference study is made in order to determine whether the growth rate of the five bacteria strains is the same. After applying a likelihood-ratio test to models with a full covariance structure, it is concluded that the specific growth rate is the same for all bacteria strains. This study highlights the importance of carrying out an explorative examination of residuals in order to make a correct parametrization of a model including the covariance structure. The ML method is shown to be a strong tool as it enables estimation of covariance parameters along with the other model parameters and it makes way for strong statistical tools for inference studies.
IEEE Transactions on Power Systems, 2013
In a real-time electricity pricing context where consumers are sensitive to varying prices, havin... more In a real-time electricity pricing context where consumers are sensitive to varying prices, having the ability to anticipate their response to a price change is valuable. This paper proposes models for the dynamics of such price-response, and shows how these dynamics can be used to control electricity consumption using a one-way price signal. Estimation of the price-response is based on data measurable at grid level, removing the need to install sensors and communication devices between each individual consumer and the price-generating entity. An application for price-responsive heating systems is studied based on real data, before conducting a control by price experiment using a mixture of real and synthetic data. With the control objective of following a constant consumption reference, peak heating consumption is reduced by nearly 5%, and 11% of the mean daily heating consumption is shifted.
Environmetrics, 1996
Data from a stream is used to identify a dynamic model of the oxygen level as a function of solar... more Data from a stream is used to identify a dynamic model of the oxygen level as a function of solar radiation and precipitation. The time series of the oxygen level is occasionally corrupted by pumping of external water into the stream, which is of no interest to the biological processes in the stream. In this paper a grey box modelling approach, which is a statistical method taking the known physical relations into account, is used. Using this approach, an identification of a stochastic continuous time model for the oxygen level based on the discrete time data, where the corrupted data are considered as missing values, is outlined. KEY WORDS oxygen dynamics; time series analysis; missing data; continuous time modelling; grey box models